Trained Quantum Neural Networks are Gaussian Processes

Explore a 25-minute conference talk from the Theory of Quantum Computation, Communication and Cryptography (TQC 2024) that delves into the mathematical properties of quantum neural networks. Discover how quantum neural networks with parametric one-qubit gates and fixed two-qubit gates behave in the infinite width limit, focusing on their convergence to Gaussian processes. Learn about the analytical characterization of network training through gradient descent with square loss on supervised learning problems, and understand how these networks can perfectly fit training sets without barren plateau effects. Examine the impact of statistical noise on measurement outputs and find out why polynomial numbers of measurements are sufficient for achieving reliable results. Gain insights into the theoretical foundations that prove these networks can be trained in polynomial time, presented by researchers Filippo Girardi and Giacomo De Palma at OIST, Japan.